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Find the area of ellipse

The problem focuses on calculating the area of an ellipse given the lengths of its major and minor axes. An ellipse is a closed curve that resembles an elongated circle. Calculating the area of an ellipse is an important mathematical computation used in various fields such as physics, engineering, and astronomy.

Problem Statement

Given the lengths of the major and minor axes of an ellipse, we need to calculate and output the area of the ellipse. The major axis is the longest diameter of the ellipse, and the minor axis is the shortest diameter that is perpendicular to the major axis.

Example

Consider an ellipse with a major axis of length 4 units and a minor axis of length 3 units. This ellipse can be visualized as follows:


      ____  
     /    \
    |      |
     \____/

Idea to Solve

To solve this problem, we can follow these steps:

  1. Calculate the area of the ellipse using the formula: π * (x_axis * y_axis), where x_axis is the length of the major axis and y_axis is the length of the minor axis.
  2. Use the provided values for the major and minor axes to compute the area.

Pseudocode

function ellipse_area(x_axis, y_axis):
    area = π * (x_axis * y_axis)
    return area

for each test case:
    x_axis, y_axis = ellipse axes lengths
    result = ellipse_area(x_axis, y_axis)
    print("Ellipse [ X-axis :", x_axis, ", Y-axis", y_axis, "]")
    print("Area :", result)

Algorithm Explanation

  1. For each test case, calculate the area of the ellipse using the provided formula.
  2. Print the ellipse's major and minor axis lengths and the calculated area.

Code Solution

//C Program
//Find the area of ellipse
#include <stdio.h>

#include <math.h>
 //Calculate area of ellipse by given axis
void ellipse_area(double x_axis, double y_axis)
{
	//Calculate Formula
	//Major and Minor Axis
	//π*(x_axis * y_axis)
	double area = (M_PI) * (x_axis * y_axis);
	//Display the result of ellipse area
	printf(" Ellipse  [ X-axis : %lf, Y-axis %lf] ", x_axis, y_axis);
	printf("\n Area : %lf\n\n", area);
}
int main()
{
	//Test Cases  
	ellipse_area(4, 3);
	ellipse_area(7, 5);
	ellipse_area(7.4, 4.2);
	return 0;
}

Output

 Ellipse  [ X-axis : 4.000000, Y-axis 3.000000]
 Area : 37.699112

 Ellipse  [ X-axis : 7.000000, Y-axis 5.000000]
 Area : 109.955743

 Ellipse  [ X-axis : 7.400000, Y-axis 4.200000]
 Area : 97.640700

// Java Program
// Find the area of ellipse
class EllipseArea
{
	//Calculate area of ellipse by given axis
	public void ellipse_area(double x_axis, double y_axis)
	{
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis * y_axis)
		double area = (Math.PI) * (x_axis * y_axis);
		//Display the result of ellipse area
		System.out.print(" Ellipse [ X-axis : " + x_axis + ", Y-axis " + y_axis + "] ");
		System.out.print("\n Area : " + area + "\n\n");
	}
	public static void main(String[] args)
	{
		EllipseArea obj = new EllipseArea();
		//Test Cases  
		obj.ellipse_area(4, 3);
		obj.ellipse_area(7, 5);
		obj.ellipse_area(7.4, 4.2);
	}
}

Output

 Ellipse [ X-axis : 4.0, Y-axis 3.0]
 Area : 37.69911184307752

 Ellipse [ X-axis : 7.0, Y-axis 5.0]
 Area : 109.95574287564276

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.64069967357078

// C++ Program
// Find the area of ellipse
#include<iostream>
#include<math.h>
using namespace std;
class EllipseArea
{
	public:
		//Calculate area of ellipse by given axis
		void ellipse_area(double x_axis, double y_axis)
		{
			//Calculate Formula
			//Major and Minor Axis
			//π*(x_axis *y_axis)
			double area = (M_PI) *(x_axis *y_axis);
			cout << " Ellipse [ X-axis : " << x_axis << ", Y-axis " << y_axis << "] ";
			cout << "\n Area : " << area << "\n\n";
		}
};
int main()
{
	EllipseArea obj = EllipseArea();
	//Test Cases  
	obj.ellipse_area(4, 3);
	obj.ellipse_area(7, 5);
	obj.ellipse_area(7.4, 4.2);
	return 0;
}

Output

 Ellipse [ X-axis : 4, Y-axis 3]
 Area : 37.6991

 Ellipse [ X-axis : 7, Y-axis 5]
 Area : 109.956

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.6407

// C# Program
// Find the area of ellipse
using System;
class EllipseArea
{
	//Calculate area of ellipse by given axis
	public void ellipse_area(double x_axis, double y_axis)
	{
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis * y_axis)
		double area = (Math.PI) * (x_axis * y_axis);
		Console.Write(" Ellipse [ X-axis : " + x_axis + ", Y-axis " + y_axis + "] ");
		Console.Write("\n Area : " + area + "\n\n");
	}
	public static void Main(String[] args)
	{
		EllipseArea obj = new EllipseArea();
		//Test Cases  
		obj.ellipse_area(4, 3);
		obj.ellipse_area(7, 5);
		obj.ellipse_area(7.4, 4.2);
	}
}

Output

 Ellipse [ X-axis : 4, Y-axis 3]
 Area : 37.6991118430775

 Ellipse [ X-axis : 7, Y-axis 5]
 Area : 109.955742875643

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.6406996735708

<?php
// Php Program
// Find the area of ellipse
class EllipseArea
{
	//Calculate area of ellipse by given axis
	public 	function ellipse_area($x_axis, $y_axis)
	{
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis *y_axis)
		$area = (M_PI) *($x_axis *$y_axis);
		//Display the result of ellipse area
		echo(" Ellipse [ X-axis : ". $x_axis .", Y-axis ". $y_axis ."] ");
		echo("\n Area : ". $area ."\n\n");
	}
}

function main()
{
	$obj = new EllipseArea();
	//Test Cases  
	$obj->ellipse_area(4, 3);
	$obj->ellipse_area(7, 5);
	$obj->ellipse_area(7.4, 4.2);
}
main();

Output

 Ellipse [ X-axis : 4, Y-axis 3]
 Area : 37.699111843078

 Ellipse [ X-axis : 7, Y-axis 5]
 Area : 109.95574287564

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.640699673571

// Node Js Program
// Find the area of ellipse
class EllipseArea
{
	//Calculate area of ellipse by given axis
	ellipse_area(x_axis, y_axis)
	{
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis *y_axis)
		var area = (Math.PI) *(x_axis *y_axis);
		//Display the result of ellipse area
		process.stdout.write(" Ellipse [ X-axis : " + x_axis + ", Y-axis " + y_axis + "] ");
		process.stdout.write("\n Area : " + area + "\n\n");
	}
}

function main(args)
{
	var obj = new EllipseArea();
	//Test Cases  
	obj.ellipse_area(4, 3);
	obj.ellipse_area(7, 5);
	obj.ellipse_area(7.4, 4.2);
}
main();

Output

 Ellipse [ X-axis : 4, Y-axis 3]
 Area : 37.69911184307752

 Ellipse [ X-axis : 7, Y-axis 5]
 Area : 109.95574287564276

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.64069967357078

#  Python 3 Program
#  Find the area of ellipse
import math
class EllipseArea :
	# Calculate area of ellipse by given axis
	def ellipse_area(self, x_axis, y_axis) :
		# Calculate Formula
		# Major and Minor Axis
		# π*(x_axis * y_axis)
		area = (math.pi) * (x_axis * y_axis)
		# Display the result of ellipse area
		print(" Ellipse [ X-axis : ", x_axis ,", Y-axis ", y_axis ,"] ")
		print(" Area : ", area ,"\n")
	

def main() :
	obj = EllipseArea()
	# Test Cases  
	obj.ellipse_area(4, 3)
	obj.ellipse_area(7, 5)
	obj.ellipse_area(7.4, 4.2)


if __name__ == "__main__": main()

Output

 Ellipse [ X-axis :  4 , Y-axis  3 ]
 Area :  37.69911184307752

 Ellipse [ X-axis :  7 , Y-axis  5 ]
 Area :  109.95574287564276

 Ellipse [ X-axis :  7.4 , Y-axis  4.2 ]
 Area :  97.64069967357078

#  Ruby Program
#  Find the area of ellipse
class EllipseArea

	# Calculate area of ellipse by given axis
	def ellipse_area(x_axis, y_axis)
	
		# Calculate Formula
		# Major and Minor Axis
		# π*(x_axis * y_axis)
		area = (Math::PI) * (x_axis * y_axis)
		# Display the result of ellipse area
		print(" Ellipse [ X-axis  :", x_axis ,", Y-axis ", y_axis ,"] ")
		print("\n Area  :", area ,"\n\n")
	end
end
def main()

	obj = EllipseArea.new()
	# Test Cases  
	obj.ellipse_area(4, 3)
	obj.ellipse_area(7, 5)
	obj.ellipse_area(7.4, 4.2)
end
main()

Output

 Ellipse [ X-axis  :4, Y-axis 3] 
 Area  :37.69911184307752

 Ellipse [ X-axis  :7, Y-axis 5] 
 Area  :109.95574287564276

 Ellipse [ X-axis  :7.4, Y-axis 4.2] 
 Area  :97.64069967357078


// Scala Program
// Find the area of ellipse
class EllipseArea
{
	//Calculate area of ellipse by given axis
	def ellipse_area(x_axis: Double, y_axis: Double): Unit = {
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis * y_axis)
		var area: Double = (Math.PI) * (x_axis * y_axis);
		//Display the result of ellipse area
		print(" Ellipse [ X-axis : " + x_axis + ", Y-axis " + y_axis + "] ");
		print("\n Area : " + area + "\n\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: EllipseArea = new EllipseArea();
		//Test Cases  
		obj.ellipse_area(4, 3);
		obj.ellipse_area(7, 5);
		obj.ellipse_area(7.4, 4.2);
	}
}

Output

 Ellipse [ X-axis : 4.0, Y-axis 3.0]
 Area : 37.69911184307752

 Ellipse [ X-axis : 7.0, Y-axis 5.0]
 Area : 109.95574287564276

 Ellipse [ X-axis : 7.4, Y-axis 4.2]
 Area : 97.64069967357078

// Swift Program
// Find the area of ellipse
class EllipseArea
{
	//Calculate area of ellipse by given axis
	func ellipse_area(_ x_axis: Double, _ y_axis: Double)
	{
		//Calculate Formula
		//Major and Minor Axis
		//π*(x_axis * y_axis)
		let area: Double = (Double.pi) * (x_axis * y_axis);
		//Display the result of ellipse area
		print(" Ellipse [ X-axis : ", x_axis ,", Y-axis ", y_axis ,"] ", terminator: "");
		print("\n Area : ", area ,"\n\n", terminator: "");
	}
}
func main()
{
	let obj: EllipseArea = EllipseArea();
	//Test Cases  
	obj.ellipse_area(4, 3);
	obj.ellipse_area(7, 5);
	obj.ellipse_area(7.4, 4.2);
}
main();

Output

 Ellipse [ X-axis :  4.0 , Y-axis  3.0 ]
 Area :  37.6991118430775

 Ellipse [ X-axis :  7.0 , Y-axis  5.0 ]
 Area :  109.955742875643

 Ellipse [ X-axis :  7.4 , Y-axis  4.2 ]
 Area :  97.6406996735708

Output Explanation

The mentioned code runs three test cases and calculates the areas of ellipses with different major and minor axis lengths. The output includes the ellipse's major and minor axis lengths and the corresponding calculated areas.

Time Complexity

The time complexity of this code is O(1) for each test case. The calculations involve basic arithmetic operations and the constant value π (pi), which take constant time. Therefore, the overall time complexity remains constant for each test case.

Last updated on by Kalkicode




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